A Roth IRA is use-it or lose-it in a sense. You can contribute up to $5500 per tax year (you have until about April to make the contribution). If you don't contribute, you're not able to make a catch-up contribution for the years you missed. In theory you can contribute this year, and then the next 2-3 years (depends how long your residency is, as when you become an attending you may make too much to be eligible to contribute to a Roth IRA). So the main disadvantage of not contributing now is you lose out on contributing $5500 to your Roth IRA.
If you have the money it makes sense to contribute now. Roth contributions are post-tax, so you get the most bang for your buck when you are hardly paying any taxes (such as your first half-year of internship when the odds are you'll get the much of your witholdings back, as you only have half a year's worth of income which that puts you in a lower tax bracket)
I'm not quite sure though what you mean by "option for beginning a Roth IRA account" or "applying" for the Roth. I just signed up with Vanguard--I don't recall any application for it other than filling out my info, and it's an individual retirement account so we all have the option to do it. Maybe there was a credit check, but I don't remember.
Here's another argument to contribute now: you can always withdraw the money (referring specifically to Roth IRAs, not the traditional ones). Now, it takes a little time, so you don't want to make your Roth your emergency fund that you might need immediate access to (you should have a few thousand in savings at least, ideally), but you can at any time withdraw up to the amount you contributed penalty-free. If you withdraw more than your contributions (this would assume your portfolio made money) then you would pay penalties on that, UNLESS you are withdrawing for a few specific reasons, like buying your "first" home (loose definition) or medical expenses, among others.
I don't personally see any reason to have 5 figures in savings first--I started a Roth with closer to $5k in savings, but I guess it depends on your comfort level. Also, if you have kids or a non-working spouse, that certainly changes things. If you can afford it, I don't see any reason to not max out your Roth every year. If you're married, don't forget the spousal IRA. And obviously if you're not on REPAYE, make sure you sign up for that before you start making retirement contributions. Doing so gives me credit towards PSLF (if it sticks around...), gets me the $2500 student loan interest deduction, and effectively halves my interest rate (almost--not quite) with the interest subsidy, so that it actually makes financial sense to put money in the Roth. (I think it's also good just to be in the habit of contributing something to your retirement account, so I'd still contribute a bit anyway even if my rates were higher).
Hopefully someone else will chime in if they disagree--I'm still new to some of the retirement stuff. But as a general rule, educate yourself and don't rely on a financial planner (read whitecoatinvestor.com, boggleheads forums, etc.). I wish I'd educated myself better as an intern. If I had, I'd have saved more, and maxed out my IRA each year. I didn't start until later in residency.
Now, before you contribute to a Roth IRA, make sure that you first max out your employer contribution for a 401k (if offered). If your employer offers a match and you don't take advantage of it, you're leaving part of your salary on the table.
